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Capital Redistribution Brings Wealth By Parrondo's Paradox
, 2002
"... this paper we introduce a new scenario for the Parrondo's paradox which involves a set of players ~ [7] and where one of the games has been replaced by a redistribution of the capital owned by the players. It will be shown that even though each individual player (when playing alone) has a negative ..."
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Cited by 8 (6 self)
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this paper we introduce a new scenario for the Parrondo's paradox which involves a set of players ~ [7] and where one of the games has been replaced by a redistribution of the capital owned by the players. It will be shown that even though each individual player (when playing alone) has a negative winning expectancy, the redistribution of money brings each player a positive expected gain. This result holds even in the case that the redistribution of capital is directed from the richer to the poorer, although in this case the distribution of money amongst the players is more uniform and the total gain is less
Discrete–time ratchets, the FokkerPlanck equation and Parrondo’s paradox
 Accepted in Proc. R. Soc. London A. Proc. of SPIE
, 2004
"... Parrondo’s games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the FokkerPlanck equation, that rigorously establish the connection between Parro ..."
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Cited by 4 (4 self)
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Parrondo’s games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the FokkerPlanck equation, that rigorously establish the connection between Parrondo’s games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo’s games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discretetime Markov chain (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs. Keywords: Parrondo’s paradox; FokkerPlanck equation; Brownian ratchet. 1.
Limit theorems and absorption problems for onedimensional correlated random walks. ArXiv Quantum Physics eprints
, 2003
"... Abstract. In this paper we consider limit theorems and absorption problems for correlated random walks determined by a 2 × 2 transition matrix on the line by using a basis P,Q,R,S of the vector space of real 2 × 2 matrices as in the case of our analysis on quantum walks. 1 ..."
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Cited by 2 (1 self)
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Abstract. In this paper we consider limit theorems and absorption problems for correlated random walks determined by a 2 × 2 transition matrix on the line by using a basis P,Q,R,S of the vector space of real 2 × 2 matrices as in the case of our analysis on quantum walks. 1
Simulation of a Quantum Random Walk
"... For my project I simulated a quantum random walk in one plus one dimensions with a ratcheting potential applied. The particle begins at the origin and after running the simulation for one hundred time steps the most probable final position was calculated and then graphed according to its initial con ..."
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For my project I simulated a quantum random walk in one plus one dimensions with a ratcheting potential applied. The particle begins at the origin and after running the simulation for one hundred time steps the most probable final position was calculated and then graphed according to its initial condition. These results were analyzed to determine the dependence on initial condition of final position.
Company c ○ World Scientific Publishing Company QUANTUM IMPLEMENTATION OF PARRONDO’S PARADOX
, 2005
"... We propose a quantum implementation of a capitaldependent Parrondo’s paradox that uses O(log2 (n)) qubits, where n is the number of Parrondo games. We present its implementation in the quantum computer language (QCL) and show simulation results. ..."
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We propose a quantum implementation of a capitaldependent Parrondo’s paradox that uses O(log2 (n)) qubits, where n is the number of Parrondo games. We present its implementation in the quantum computer language (QCL) and show simulation results.
unknown title
, 2009
"... Limit theorems and absorption problems for onedimensional correlated random walks ..."
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Limit theorems and absorption problems for onedimensional correlated random walks
unknown title
, 2008
"... Limit theorems and absorption problems for onedimensional correlated random walks ..."
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Limit theorems and absorption problems for onedimensional correlated random walks
An Investigation of Quantum Computational Game Theory
, 2006
"... Game theory is a well established field with applications in many areas including the social sciences, biology, and computer science [6]. Recently, however, researchers in quantum computation have begun to study the implications of games set in the quantum domain (i.e. game theoretical situations wh ..."
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Game theory is a well established field with applications in many areas including the social sciences, biology, and computer science [6]. Recently, however, researchers in quantum computation have begun to study the implications of games set in the quantum domain (i.e. game theoretical situations where either one or more players have quantum computational power or where the implementation of strategies uses some form of quantum information). Such a setting allows for entanglement and superpositions of strategies and evaluation of payoffs using quantum measurement. This approach to game theory, according to some scholars in the field, could help us understand certain physical systems, improve economic markets, and develop quantum algorithms. I have conducted an investigation into quantum game theory. I have constructed simulation tools using Maple that, along with research into related work, have helped gain some insight into this new field. The important solutions in classical game theory are usually Nash equilibria. What do they look like in the quantum realm? In what